Is heat a process or a term for energy in transit? 2 definitions I have come across:

*

*Heat is the transfer of energy into or out of a thermodynamic system by a process that isn't thermodynamic work or transfer of matter


*Heat is the energy transferred into  or out of a thermodynamic system by a process that ins't thermodynamic work or transfer of matter
I am clear on the difference between heat and internal energy, a state function which doesn't care about how the energy was added or removed. My confusion is whether heat refers to a process or the energy in transit. I have seen most authors use the 2nd definition. But then I came across this article which by Zemansky where he argues otherwise. https://www.deepdyve.com/lp/american-association-of-physics-teachers/the-use-and-misuse-of-the-word-heat-in-physics-teaching-02AsHIMVbq
This is similar to the fact that a current does't flow, charge does; everybody gets the idea so its a harmless mistake at best. But if I want to be accurate, what's the general consensus among physicists ?
 A: 
My confusion is whether heat refers to a process or the energy in
transit.

It refers to energy in transit, not to a process. Multiple processes can be involved with heat transfer. For example, for gases you can have heat transfer by means of a constant pressure process or a constant volume process. Similarly, work refers to energy in transit, not a process.
More importantly, and missing from your two definitions, is that heat is the transfer of energy due solely to temperature difference. The statement "temperature difference" is key to the definition of heat and is missing from both of your definitions. It is what differentiates heat from work. The latter does not require a temperature difference.

I thought the temperature difference was just a fact abt heat that
comes from the 2nd law of thermodynamics and not something defining
heat.

Temperature difference does not define heat. It is a minimum necessary (but not sufficient) condition for energy transfer to occur in the form of heat.
You can have a temperature difference between objects and no energy transfer in the form of heat if there is no mechanism that allows the transfer to occur. Conduction requires contact between the objects, convection requires the movement of a fluid in contact with the surface of an object, and radiation requires an unobstructed path between objects. If the two objects at different temperatures are isolated from one another, there can be no energy transfer in the form of heat.

More importantly, it uses "temperature" to define heat and temperature
itself is defined as being "some property" that becomes equal when
there is no net flow of heat. Wouldn't that make it circular?

It doesn't use temperature to define heat. It states that temperature difference is a condition required for energy transfer in the form of heat to occur. The temperatures do not become equal when there is no net flow of heat. As already indicated, a difference in temperature does not necessarily result in heat flow. However, there can be no heat flow if the temperatures are equal. In my opinion there is no circular reasoning here.
Hope this helps.
A: I find these definitions from Obert and Young, Elements of Thermodynamics and Heat Transfer, to be useful.
"Heat is energy transferred, without mass transfer, across the boundaries of a system solely because of a difference in temperature between system and surroundings."
"Work is energy transferred, without mass transfer, across the boundaries of a system because of an intensive property difference other than temperature between system and surroundings."
One source of confusion is a mis-use of the term "heat" to refer to the energy content within a system; the correct term is internal energy.  Heat, like work, is energy transferred across a boundary.  It makes no more sense to refer to the heat in a body than to refer to the work in a body.
Both heat and work exclude mass transfer.  In thermodynamics a system with mass transfer in/out is an called an open system and the energy balance accounts for the energy associated with mass flowing in/out in addition to heat and work.
Work as defined in thermodynamics is much broader concept than work defined for the dynamics of motion.  In mechanics work is restricted to the change in kinetic energy due to a force acting through a distance, and does not address changes in internal energy.
(For a conservative force, such as gravity or an electrostatic field, the mechanical work is typically considered as a change in potential energy.)
